The poll also found that a plurality of voters support the Affordable Care Act, also known as ObamaCare. Almost half of voters, 47 percent, said they approve of the health care law, compared to 41 percent who said they disapprove of it.

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Additionally, 45 percent of voters said they trust Democrats more than Republicans in Congress on health care, while 35 percent said they have more trust in Republicans.

"As health care is pushed to the forefront of the 2020 agenda, our polling suggests President Trump may struggle to attract voters with his promise of a new plan,” Tyler Sinclair, Morning Consult’s vice president, told Politico.

The findings come after the Trump administration last week called for the entirety of the Affordable Care Act to be struck down. Trump pledged that Republicans would become the "party of health care" and said the GOP would come up with a “far better” health care proposal than ObamaCare.

“I made clear to him that we were not going to be doing that in the Senate,” McConnell said he told the president. “He did say, as he later tweeted, that he accepted that and he would be developing a plan that he would take to the American people during the 2020 campaign.”

Trump said Monday night that Republicans were developing a health care plan and that a vote will be taken following next year's elections.